2021학년도 1학기 (3월~8월)

B K21  기 하 학 수 요 집 회

과 학 관 254 호, 수요일, 15:00 pm (격주) 

ZOOM 회의실 링크:  

Abstract: This talk is about higher Du Bois singularities. The first part briefly reviews the theory of mixed Hodge modules developed by Morihiko Saito. The second part is devoted to introducing the notion of higher Du Bois singularities. The main point of this part is its relationship with the minimal exponent of hypersurface singularities. This is based on joint work with I.-K. Kim, M. Saito and Y. Yoon.

유리 곡선, 그 어느 곳에서나... (Sci.Hall 254 & ZOOM, 50+50min)

주제: BK 기하학 수요세미나 (정기용 교수) 6월 9일
시간: 2021년 6월 9일  02:30 오후 서울

Zoom 회의 참가 링크:   https://yonsei.zoom.us/j/89791602146
회의 ID: 897 9160 2146

종수가 0인 대수적 곡선을 유리곡선이라 한다. 이 곡선은 대수기하학의 거의 모든 세부 분야에서 출현하는 매우 친숙한 대상이다. 본 강의에서는 유리곡선의 대수 방정식 찾는 문제를 출발로 하여, 힐베르트 스킴, 안정화된 쉬프 및 사상들의 모듈리 공간의 개념을 소개한다. 이후, 그라시마니안 속의 유리곡선들의 모듈리를 탐구하여, 그라시마니안의 선형절단된 파노 다양체에서 Donaldson -Thomas 불변량을 계산한다. 이것은 기존의 Gromov-Witten 불변량과 관계성을 수학적 관점에서 옳다는 것을 말해주는 좋은 예이다. 셈기하학의 매우 구체적인 예를 제시하는 것으로, 컴퓨터 프로그램을 구동 시켜 보기도 할 것이다.

Symplectic Structures Associated to Lie Groups (Sci.Hall 254 & ZOOM , 90min+)

I will first give a brief overview on the structure of semisimple Lie groups and their Lie algebras. Then I will discuss how to understand the symplectic structures on the cotangent bundles of semisimple Lie groups and those on the flag varieties in terms of the corresponding Lie algebra.

Kaehler-Einstein Metrics  (Sci.Hall 254 & ZOOM, 90min)

In differential geometry, an important problem is to prove the existence of Kaehler-Einstein metrics for compact Kaehler manifolds.  It has grown into a very rich subject with deep connections to nonlinear PDE, geometric analysis and complex algebraic geometry. In this talk, I will give an overview of some of these developments and results.

Disc Potential Functions and Toric Degenerations (Sci.Hall 254 & ZOOM , 90min) 

The disc potentials introduced by Fukaya-Oh-Ohta-Ono have played a pivotal role in Lagrangian Floer theory and mirror symmetry.  After explaining how to define disc potentials, we compute disc potentials via explicit examples on toric manifolds. Then we discuss how to compute the disc potentials of generic fibers of toric degenerations arising from certain Newton-Okounkov bodies.

Geometry of Nodal Surfaces (ZOOM, 90 min)

We consider irreducible surfaces in $\mathbb{P}^3$ having singularities at worst nodes. It has been an intriguing question to ask how many nodes such surfaces may possess. This number is only known for small degrees. For instance, if surface has degree 6, then the maximal number of nodes is 65, and is realized by the Barth's sextic. One of the typical approach to study such surfaces is to investigate the even sets of nodes. We are going to explain what are even sets of nodes, and why they are useful for the study of nodal surfaces. Also, we will discuss the structure of even sets of nodes on Barth's sextic, and the possible application of these data. This talk is based on the joint work with Fabrizio Catanese, Michael Kiermaier, and Sascha Kurz.